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A dust mite allergen level that exceeds 2 micrograms per gram ( \"g / g ) of dust has been associated with the development of allergies. Consider a random sample of 4 homes. Let x = number of homes with a dust mite allergen level that exceeds 2 \"g I g . The probability distribution for x is given below. 3' 0 l 2 3 4 P(x) 0.09 0.30 0.37 0.20 0.04 a. Find the probability that at least three of the homes have a dust mite level that exceeds 2 \"3 I 3 . b. Find the probability that fewer that two of the homes have a dust mite level that exceeds 2 \"g I g . c. Compute and interpret it . d. Construct the interval V' =20 , determine the probability x falls in that interval, and compare your answer to Chebyshevis Theorem